The fractal cosmological model

TL;DR

This paper proposes a fractal cosmological model where the Universe's large-scale structure's fractal properties arise from a self-similar arrangement of space-time domains governed by a charged scalar meson field, maintaining fractality through gravitational evolution.

Contribution

It introduces a novel fractal cosmological model based on scale-invariant solutions of Einstein's equations with a charged scalar field, explaining the Universe's fractal large-scale structure.

Findings

Found scale-invariant solutions of Einstein's and field equations.

Demonstrated fractal properties are preserved during gravitational evolution.

Explained fractal large-scale structure through self-similar space-time domains.

Abstract

The fractal cosmological model which accounts for observable fractal properties of the Universe's large-scale structure is constructed. In this framework these properties are consequences of the rotary symmetry of charged scalar meson matter field (complex field). They may be explained through a conception of the Universe as an assembly of self-similar space-time domains. We have found the scale invariant solutions of Einstein's equation and Lagrange's field equation. For the solution the space-time domains with field values related by the scaling are geometrically similar and evolve similarly. Due to this, fractal properties of initial density perturbations which lead to formation of the large-scale structure remain during the gravitational evolution and lead to presence of the fractal properties in the large-scale structure.